(* -------------------------------------------------------------------------- *)
-(* File : LCL156-1 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : LCL156-1 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Logic Calculi (Wajsberg Algebra) *)
(* -------------------------------------------------------------------------- *)
-(* File : LCL001-0 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : LCL001-0 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Logic Calculi (Wajsberg Algebras) *)
(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 0 RR) *)
-(* Number of literals : 4 ( 4 equality) *)
+(* Number of atoms : 4 ( 4 equality) *)
(* Maximal clause size : 1 ( 1 average) *)
(* -------------------------------------------------------------------------- *)
-(* File : LCL001-2 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : LCL001-2 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Logic Calculi (Wajsberg Algebras) *)
(* Syntax : Number of clauses : 6 ( 0 non-Horn; 6 unit; 0 RR) *)
-(* Number of literals : 6 ( 6 equality) *)
+(* Number of atoms : 6 ( 6 equality) *)
(* Maximal clause size : 1 ( 1 average) *)
(* -------------------------------------------------------------------------- *)
-(* File : LCL002-1 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : LCL002-1 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Logic Calculi (Wajsberg Algebras) *)
(* Syntax : Number of clauses : 6 ( 0 non-Horn; 6 unit; 1 RR) *)
-(* Number of literals : 6 ( 6 equality) *)
+(* Number of atoms : 6 ( 6 equality) *)
(* Maximal clause size : 1 ( 1 average) *)
(* -------------------------------------------------------------------------- *)
ntheorem prove_alternative_wajsberg_axiom:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀myand:∀_:Univ.∀_:Univ.Univ.
∀and_star:∀_:Univ.∀_:Univ.Univ.
∀falsehood:Univ.
∀H12:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
∀H13:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
-∀H15:∀X:Univ.eq Univ (implies truth X) X.eq Univ (and_star x truth) x
+∀H15:∀X:Univ.eq Univ (implies truth X) X.eq Univ (and_star x truth) x)
.
-#Univ.
-#X.
-#Y.
-#Z.
-#and.
-#and_star.
-#falsehood.
-#implies.
-#not.
-#or.
-#truth.
-#x.
-#xor.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-#H15.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#myand ##.
+#and_star ##.
+#falsehood ##.
+#implies ##.
+#not ##.
+#or ##.
+#truth ##.
+#x ##.
+#xor ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+#H15 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##;
+ntry (nassumption) ##;
nqed.
(* -------------------------------------------------------------------------- *)